GATE 2021 AR – Question 58

Building Services · Principles of electrification and illumination and special lighting for buildings · 2 marks · Numerical answer

A 180 m diameter circular cricket field has four equally spaced perimeter floodlight towers 48 m high. Each tower has fifty 700 W lamps. Centre illumination is 750 lux. Using the inverse-square model, find lamp efficacy in lm/W, to two decimals.

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Show answer and explanation

Correct answer: 117.00 to 119.00 OR 1483.00 to 1496.00

Explanation

Source ambiguity is reflected in two official ranges. Horizontal distance is 90 m; slant distance is√(90²+48²)=102 m and incidence cosine is 48/102. Dividing E×102² by the incidence cosine and by 200 lamps gives 82906.875 cd per lamp. Intensity per electrical watt is 118.44 cd/W, within the first range. Converting isotropic intensity to flux by 4π gives 1488.34 lm/W, within the second range. Actual directional floodlights require their beam distribution/solid angle, which the question does not specify; cd/W and lm/W are distinct quantities.

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